ICM25¶
Analysis of the long-term evolution of international equity markets (average returns, volatilities, long-term correlations) and economic risks of European stock markets.
Case 1: Analyzing 25 years of stock market returns¶
Analysis of the longterm evolution of international equity markets, i.e.
- Average returns
- Volatilities
- Long-term correlations between markets
- Correlation regimes
Data set (Case1.csv) includes 16 stock market indices in local currencies covering developed markets in North America, Europe and Asia-Pacific
- Monthly stock market data starting on December 31, 1992, and ending on February 28, 2018
- Indexed to ”100” at the beginning of the period
In [1]:
import math
import numpy as np
import pandas as pd
import plotly.express as px
In [2]:
# Metadata
data = pd.read_csv('data/Case1.csv')
# print(data.info())
# print(data.describe())
data['Date'] = pd.to_datetime(data['Date'])
- Display the long-term performance of the equity markets
In [3]:
data_melted = data.melt(id_vars=['Date'], value_vars=data.columns[1:], var_name='Index', value_name='Value')
fig = px.line(data_melted, x='Date', y='Value', color='Index', title='Long-term performance of the equity markets', log_y=True)
fig.show()
- Calculate mean returns and volatilities over the total period
In [4]:
returns = data.copy()
for index in data.columns[1:]:
for i in range(1, len(data[index])):
returns.loc[i, index] = np.log(data.loc[i, index] / data.loc[i - 1, index])
# First row needs to be removed as it is 100% return
returns = returns.drop(0)
# print(returns.info())
# print(returns.head())
# Mean and SD (volatility) of the returns
results_list = []
for index in returns.columns[1:]:
mean_return = math.exp(returns[index].mean()*12)-1
std_return = returns[index].std()*math.sqrt(12)
results_list.append({'Index': index, 'Mean Return p.a.': mean_return, 'Volatility': std_return})
results = pd.DataFrame(results_list)
results_melted = results.melt(id_vars='Index', value_vars=['Mean Return p.a.', 'Volatility'], var_name='Metric', value_name='Value')
fig = px.bar(results_melted, x='Index', y='Value', color='Metric', barmode='group', title='Mean returns p.a. and volatilities')
fig.show()
- Calculate yearly returns for the stock markets
In [5]:
returns['Year'] = returns['Date'].dt.year
grouped_returns = returns.drop(columns=['Date']).groupby('Year').sum().reset_index()
fig = px.line(grouped_returns, x='Year', y=grouped_returns.columns[1:], title='Yearly returns for the stock markets')
fig.show()
- Calculate the correlations between the markets over the period 1993-2017
In [6]:
correlation_matrix = returns.drop(columns=['Date', 'Year']).corr()
correlation_matrix.loc['Mean'] = correlation_matrix.mean(axis=1)
fig = px.imshow(correlation_matrix, text_auto=True, title='Correlation Matrix (full)', color_continuous_scale='RdBu_r')
fig.show()
- Calculate the correlations for five sub-periods and analyze the correlation regimes
- 1993-1997
- 1998-2002
- 2003-2007
- 2008-2012
- 2013-2017
In [7]:
correlation_matrix_avg = pd.DataFrame()
time_delta = 4
for year in range(1993, 2018, time_delta):
returns_sub = returns[returns['Year'].between(year, year+time_delta)]
correlation_matrix = returns_sub.drop(columns=['Date', 'Year']).corr()
correlation_matrix_avg[f'{year}-{year + time_delta}'] = correlation_matrix.mean()
fig = px.imshow(correlation_matrix, text_auto=True, title=f'Correlation Matrix ({year}-{year + time_delta})', color_continuous_scale='RdBu_r', zmin=0, zmax=1)
fig.show()
fig = px.imshow(correlation_matrix_avg, text_auto=True, title='Average correlation over sub-periods', color_continuous_scale='RdBu_r', zmin=0, zmax=1)
fig.show()
Case 2: Rational asset pricing and multifactor models¶
Data set (Case2Factors.csv and Case2MSCI.csv) include monthly total return index data over the 1st decade of the 21st century, from January 2000 to December 2009, denominated in EUR for 10 European stock markets and 4 global risk factors.
Case2.py analyzes the relationships between the returns of the stock markets and the changes of the global factors using the following regressions for each market:
- Market return on the MSCI World index return (single factor model)
- Market return on the 4 global factors (4-factor model)
In [8]:
import numpy as np
import pandas as pd
import statsmodels.api as sm
Prepare MSCI world return data (Switzerland, Germany, France, UK, Japan, USA)
In [9]:
dataMSCI = pd.read_csv('data/Case2MSCI.csv')
# print(dataMSCI.info())
# print(dataMSCI.describe())
dataMSCI['Date'] = pd.to_datetime(dataMSCI['Date'])
returnsMSCI = dataMSCI.copy()
for index in dataMSCI.columns[1:]:
for i in range(1, len(dataMSCI[index])):
returnsMSCI.loc[i, index] = np.log(dataMSCI.loc[i, index] / dataMSCI.loc[i - 1, index])
# First row needs to be removed as it is 100% return
returnsMSCI = returnsMSCI.drop(0)
# print(returnsMSCI.info())
# print(returnsMSCI.head())
Prepare global factors return data (MSCI World, CRB Index, EUR 10Y Rate, FX USD/EUR)
In [10]:
dataFactors = pd.read_csv('data/Case2Factors.csv')
# print(dataFactors.info())
# print(dataFactors.describe())
dataFactors['Date'] = pd.to_datetime(dataFactors['Date'])
returnsFactors = dataFactors.copy()
for index in dataFactors.columns[1:]:
for i in range(1, len(dataFactors[index])):
returnsFactors.loc[i, index] = np.log(dataFactors.loc[i, index] / dataFactors.loc[i - 1, index])
# First row needs to be removed as it is 100% return
returnsFactors = returnsFactors.drop(0)
# print(returnsFactors.info())
# print(returnsFactors.head())
Market return on the MSCI World index return (single factor model)
In [11]:
for country in returnsMSCI.columns[1:]:
y = returnsMSCI[country]
X = returnsFactors['MSCI World']
# Add a constant to the independent variable
X = sm.add_constant(X)
model = sm.OLS(y, X).fit()
print(f"\n\n{"="*32} {country} {"="*33}")
print(model.summary())
================================ Switzerland =================================
OLS Regression Results
==============================================================================
Dep. Variable: Switzerland R-squared: 0.631
Model: OLS Adj. R-squared: 0.628
Method: Least Squares F-statistic: 202.0
Date: Sun, 11 Aug 2024 Prob (F-statistic): 2.50e-27
Time: 22:49:09 Log-Likelihood: 273.35
No. Observations: 120 AIC: -542.7
Df Residuals: 118 BIC: -537.1
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
const 0.0032 0.002 1.404 0.163 -0.001 0.008
MSCI World 0.6919 0.049 14.214 0.000 0.596 0.788
==============================================================================
Omnibus: 1.468 Durbin-Watson: 1.809
Prob(Omnibus): 0.480 Jarque-Bera (JB): 1.024
Skew: -0.018 Prob(JB): 0.599
Kurtosis: 3.451 Cond. No. 21.3
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
================================ Germany =================================
OLS Regression Results
==============================================================================
Dep. Variable: Germany R-squared: 0.726
Model: OLS Adj. R-squared: 0.724
Method: Least Squares F-statistic: 312.7
Date: Sun, 11 Aug 2024 Prob (F-statistic): 5.74e-35
Time: 22:49:09 Log-Likelihood: 227.65
No. Observations: 120 AIC: -451.3
Df Residuals: 118 BIC: -445.7
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
const 0.0021 0.003 0.632 0.529 -0.005 0.009
MSCI World 1.2598 0.071 17.683 0.000 1.119 1.401
==============================================================================
Omnibus: 14.964 Durbin-Watson: 2.272
Prob(Omnibus): 0.001 Jarque-Bera (JB): 30.839
Skew: -0.472 Prob(JB): 2.01e-07
Kurtosis: 5.297 Cond. No. 21.3
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
================================ UK =================================
OLS Regression Results
==============================================================================
Dep. Variable: UK R-squared: 0.826
Model: OLS Adj. R-squared: 0.824
Method: Least Squares F-statistic: 559.2
Date: Sun, 11 Aug 2024 Prob (F-statistic): 1.37e-46
Time: 22:49:09 Log-Likelihood: 303.42
No. Observations: 120 AIC: -602.8
Df Residuals: 118 BIC: -597.3
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
const 0.0007 0.002 0.369 0.712 -0.003 0.004
MSCI World 0.8960 0.038 23.647 0.000 0.821 0.971
==============================================================================
Omnibus: 5.877 Durbin-Watson: 2.333
Prob(Omnibus): 0.053 Jarque-Bera (JB): 5.334
Skew: -0.458 Prob(JB): 0.0695
Kurtosis: 3.477 Cond. No. 21.3
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
================================ Sweden =================================
OLS Regression Results
==============================================================================
Dep. Variable: Sweden R-squared: 0.652
Model: OLS Adj. R-squared: 0.649
Method: Least Squares F-statistic: 220.9
Date: Sun, 11 Aug 2024 Prob (F-statistic): 8.32e-29
Time: 22:49:09 Log-Likelihood: 194.41
No. Observations: 120 AIC: -384.8
Df Residuals: 118 BIC: -379.3
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
const 0.0029 0.004 0.659 0.511 -0.006 0.012
MSCI World 1.3969 0.094 14.864 0.000 1.211 1.583
==============================================================================
Omnibus: 12.053 Durbin-Watson: 2.158
Prob(Omnibus): 0.002 Jarque-Bera (JB): 34.968
Skew: 0.058 Prob(JB): 2.55e-08
Kurtosis: 5.642 Cond. No. 21.3
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
================================ Norway =================================
OLS Regression Results
==============================================================================
Dep. Variable: Norway R-squared: 0.555
Model: OLS Adj. R-squared: 0.551
Method: Least Squares F-statistic: 146.9
Date: Sun, 11 Aug 2024 Prob (F-statistic): 1.85e-22
Time: 22:49:09 Log-Likelihood: 182.68
No. Observations: 120 AIC: -361.4
Df Residuals: 118 BIC: -355.8
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
const 0.0101 0.005 2.069 0.041 0.000 0.020
MSCI World 1.2562 0.104 12.122 0.000 1.051 1.461
==============================================================================
Omnibus: 27.978 Durbin-Watson: 1.688
Prob(Omnibus): 0.000 Jarque-Bera (JB): 57.320
Skew: -0.955 Prob(JB): 3.57e-13
Kurtosis: 5.796 Cond. No. 21.3
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
================================ France =================================
OLS Regression Results
==============================================================================
Dep. Variable: France R-squared: 0.786
Model: OLS Adj. R-squared: 0.784
Method: Least Squares F-statistic: 434.0
Date: Sun, 11 Aug 2024 Prob (F-statistic): 2.41e-41
Time: 22:49:09 Log-Likelihood: 269.52
No. Observations: 120 AIC: -535.0
Df Residuals: 118 BIC: -529.5
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
const 0.0021 0.002 0.892 0.374 -0.003 0.007
MSCI World 1.0470 0.050 20.833 0.000 0.947 1.147
==============================================================================
Omnibus: 2.279 Durbin-Watson: 2.394
Prob(Omnibus): 0.320 Jarque-Bera (JB): 2.014
Skew: -0.045 Prob(JB): 0.365
Kurtosis: 3.628 Cond. No. 21.3
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
================================ Italy =================================
OLS Regression Results
==============================================================================
Dep. Variable: Italy R-squared: 0.630
Model: OLS Adj. R-squared: 0.627
Method: Least Squares F-statistic: 201.2
Date: Sun, 11 Aug 2024 Prob (F-statistic): 2.89e-27
Time: 22:49:09 Log-Likelihood: 235.38
No. Observations: 120 AIC: -466.8
Df Residuals: 118 BIC: -461.2
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
const 0.0014 0.003 0.446 0.657 -0.005 0.008
MSCI World 0.9476 0.067 14.186 0.000 0.815 1.080
==============================================================================
Omnibus: 8.166 Durbin-Watson: 2.093
Prob(Omnibus): 0.017 Jarque-Bera (JB): 15.022
Skew: -0.169 Prob(JB): 0.000547
Kurtosis: 4.700 Cond. No. 21.3
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
================================ Spain =================================
OLS Regression Results
==============================================================================
Dep. Variable: Spain R-squared: 0.646
Model: OLS Adj. R-squared: 0.643
Method: Least Squares F-statistic: 215.0
Date: Sun, 11 Aug 2024 Prob (F-statistic): 2.38e-28
Time: 22:49:09 Log-Likelihood: 230.99
No. Observations: 120 AIC: -458.0
Df Residuals: 118 BIC: -452.4
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
const 0.0066 0.003 2.034 0.044 0.000 0.013
MSCI World 1.0159 0.069 14.662 0.000 0.879 1.153
==============================================================================
Omnibus: 0.012 Durbin-Watson: 2.125
Prob(Omnibus): 0.994 Jarque-Bera (JB): 0.120
Skew: 0.012 Prob(JB): 0.942
Kurtosis: 2.847 Cond. No. 21.3
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
================================ Netherlands =================================
OLS Regression Results
==============================================================================
Dep. Variable: Netherlands R-squared: 0.763
Model: OLS Adj. R-squared: 0.761
Method: Least Squares F-statistic: 380.5
Date: Sun, 11 Aug 2024 Prob (F-statistic): 1.01e-38
Time: 22:49:09 Log-Likelihood: 249.86
No. Observations: 120 AIC: -495.7
Df Residuals: 118 BIC: -490.2
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
const 0.0018 0.003 0.665 0.508 -0.004 0.007
MSCI World 1.1548 0.059 19.506 0.000 1.038 1.272
==============================================================================
Omnibus: 3.142 Durbin-Watson: 2.120
Prob(Omnibus): 0.208 Jarque-Bera (JB): 2.607
Skew: -0.339 Prob(JB): 0.272
Kurtosis: 3.247 Cond. No. 21.3
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
================================ Austria =================================
OLS Regression Results
==============================================================================
Dep. Variable: Austria R-squared: 0.372
Model: OLS Adj. R-squared: 0.367
Method: Least Squares F-statistic: 69.89
Date: Sun, 11 Aug 2024 Prob (F-statistic): 1.43e-13
Time: 22:49:09 Log-Likelihood: 172.24
No. Observations: 120 AIC: -340.5
Df Residuals: 118 BIC: -334.9
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
const 0.0061 0.005 1.153 0.251 -0.004 0.017
MSCI World 0.9451 0.113 8.360 0.000 0.721 1.169
==============================================================================
Omnibus: 42.561 Durbin-Watson: 1.424
Prob(Omnibus): 0.000 Jarque-Bera (JB): 193.645
Skew: -1.099 Prob(JB): 8.92e-43
Kurtosis: 8.822 Cond. No. 21.3
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
Market return on the 4 global factors (4-factor model)
In [12]:
for country in returnsMSCI.columns[1:]:
y = returnsMSCI[country]
X = returnsFactors[['FX USD/EUR', 'EUR 10Y Rate' ,'CRB Index', 'MSCI World']]
# Add a constant to the independent variable
X = sm.add_constant(X)
model = sm.OLS(y, X).fit()
print(f"\n\n{"="*32} {country} {"="*33}")
print(model.summary())
================================ Switzerland =================================
OLS Regression Results
==============================================================================
Dep. Variable: Switzerland R-squared: 0.674
Model: OLS Adj. R-squared: 0.662
Method: Least Squares F-statistic: 59.37
Date: Sun, 11 Aug 2024 Prob (F-statistic): 4.25e-27
Time: 22:49:09 Log-Likelihood: 280.69
No. Observations: 120 AIC: -551.4
Df Residuals: 115 BIC: -537.4
Df Model: 4
Covariance Type: nonrobust
================================================================================
coef std err t P>|t| [0.025 0.975]
--------------------------------------------------------------------------------
const 0.0035 0.002 1.565 0.120 -0.001 0.008
FX USD/EUR 0.2081 0.075 2.759 0.007 0.059 0.358
EUR 10Y Rate 0.0626 0.052 1.206 0.230 -0.040 0.165
CRB Index -0.1146 0.048 -2.383 0.019 -0.210 -0.019
MSCI World 0.7431 0.053 14.017 0.000 0.638 0.848
==============================================================================
Omnibus: 4.731 Durbin-Watson: 1.689
Prob(Omnibus): 0.094 Jarque-Bera (JB): 4.503
Skew: 0.314 Prob(JB): 0.105
Kurtosis: 3.711 Cond. No. 35.2
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
================================ Germany =================================
OLS Regression Results
==============================================================================
Dep. Variable: Germany R-squared: 0.807
Model: OLS Adj. R-squared: 0.800
Method: Least Squares F-statistic: 120.4
Date: Sun, 11 Aug 2024 Prob (F-statistic): 3.73e-40
Time: 22:49:09 Log-Likelihood: 248.73
No. Observations: 120 AIC: -487.5
Df Residuals: 115 BIC: -473.5
Df Model: 4
Covariance Type: nonrobust
================================================================================
coef std err t P>|t| [0.025 0.975]
--------------------------------------------------------------------------------
const 0.0019 0.003 0.655 0.514 -0.004 0.008
FX USD/EUR 0.5952 0.098 6.046 0.000 0.400 0.790
EUR 10Y Rate 0.1419 0.068 2.094 0.038 0.008 0.276
CRB Index -0.1684 0.063 -2.684 0.008 -0.293 -0.044
MSCI World 1.3622 0.069 19.686 0.000 1.225 1.499
==============================================================================
Omnibus: 16.175 Durbin-Watson: 2.404
Prob(Omnibus): 0.000 Jarque-Bera (JB): 40.147
Skew: -0.438 Prob(JB): 1.92e-09
Kurtosis: 5.695 Cond. No. 35.2
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
================================ UK =================================
OLS Regression Results
==============================================================================
Dep. Variable: UK R-squared: 0.839
Model: OLS Adj. R-squared: 0.834
Method: Least Squares F-statistic: 150.0
Date: Sun, 11 Aug 2024 Prob (F-statistic): 1.16e-44
Time: 22:49:09 Log-Likelihood: 308.22
No. Observations: 120 AIC: -606.4
Df Residuals: 115 BIC: -592.5
Df Model: 4
Covariance Type: nonrobust
================================================================================
coef std err t P>|t| [0.025 0.975]
--------------------------------------------------------------------------------
const 0.0005 0.002 0.279 0.781 -0.003 0.004
FX USD/EUR 0.1063 0.060 1.772 0.079 -0.013 0.225
EUR 10Y Rate 0.0983 0.041 2.381 0.019 0.017 0.180
CRB Index 0.0334 0.038 0.875 0.384 -0.042 0.109
MSCI World 0.8620 0.042 20.452 0.000 0.779 0.946
==============================================================================
Omnibus: 7.626 Durbin-Watson: 2.411
Prob(Omnibus): 0.022 Jarque-Bera (JB): 7.234
Skew: -0.550 Prob(JB): 0.0269
Kurtosis: 3.489 Cond. No. 35.2
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
================================ Sweden =================================
OLS Regression Results
==============================================================================
Dep. Variable: Sweden R-squared: 0.696
Model: OLS Adj. R-squared: 0.685
Method: Least Squares F-statistic: 65.68
Date: Sun, 11 Aug 2024 Prob (F-statistic): 8.24e-29
Time: 22:49:09 Log-Likelihood: 202.46
No. Observations: 120 AIC: -394.9
Df Residuals: 115 BIC: -381.0
Df Model: 4
Covariance Type: nonrobust
================================================================================
coef std err t P>|t| [0.025 0.975]
--------------------------------------------------------------------------------
const 0.0018 0.004 0.424 0.673 -0.007 0.010
FX USD/EUR 0.5744 0.145 3.968 0.000 0.288 0.861
EUR 10Y Rate 0.0408 0.100 0.409 0.683 -0.157 0.238
CRB Index -0.0427 0.092 -0.463 0.644 -0.226 0.140
MSCI World 1.4895 0.102 14.639 0.000 1.288 1.691
==============================================================================
Omnibus: 22.814 Durbin-Watson: 2.313
Prob(Omnibus): 0.000 Jarque-Bera (JB): 94.146
Skew: 0.465 Prob(JB): 3.60e-21
Kurtosis: 7.238 Cond. No. 35.2
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
================================ Norway =================================
OLS Regression Results
==============================================================================
Dep. Variable: Norway R-squared: 0.747
Model: OLS Adj. R-squared: 0.738
Method: Least Squares F-statistic: 84.70
Date: Sun, 11 Aug 2024 Prob (F-statistic): 2.31e-33
Time: 22:49:09 Log-Likelihood: 216.51
No. Observations: 120 AIC: -423.0
Df Residuals: 115 BIC: -409.1
Df Model: 4
Covariance Type: nonrobust
================================================================================
coef std err t P>|t| [0.025 0.975]
--------------------------------------------------------------------------------
const 0.0065 0.004 1.735 0.085 -0.001 0.014
FX USD/EUR 0.9059 0.129 7.036 0.000 0.651 1.161
EUR 10Y Rate 0.3405 0.089 3.843 0.000 0.165 0.516
CRB Index 0.4185 0.082 5.098 0.000 0.256 0.581
MSCI World 1.1142 0.091 12.311 0.000 0.935 1.293
==============================================================================
Omnibus: 15.924 Durbin-Watson: 1.868
Prob(Omnibus): 0.000 Jarque-Bera (JB): 33.019
Skew: -0.509 Prob(JB): 6.76e-08
Kurtosis: 5.360 Cond. No. 35.2
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
================================ France =================================
OLS Regression Results
==============================================================================
Dep. Variable: France R-squared: 0.852
Model: OLS Adj. R-squared: 0.847
Method: Least Squares F-statistic: 165.6
Date: Sun, 11 Aug 2024 Prob (F-statistic): 9.55e-47
Time: 22:49:09 Log-Likelihood: 291.60
No. Observations: 120 AIC: -573.2
Df Residuals: 115 BIC: -559.3
Df Model: 4
Covariance Type: nonrobust
================================================================================
coef std err t P>|t| [0.025 0.975]
--------------------------------------------------------------------------------
const 0.0014 0.002 0.676 0.500 -0.003 0.005
FX USD/EUR 0.4732 0.069 6.872 0.000 0.337 0.610
EUR 10Y Rate 0.0582 0.047 1.228 0.222 -0.036 0.152
CRB Index -0.0556 0.044 -1.266 0.208 -0.143 0.031
MSCI World 1.1211 0.048 23.160 0.000 1.025 1.217
==============================================================================
Omnibus: 12.951 Durbin-Watson: 2.605
Prob(Omnibus): 0.002 Jarque-Bera (JB): 29.042
Skew: 0.342 Prob(JB): 4.94e-07
Kurtosis: 5.311 Cond. No. 35.2
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
================================ Italy =================================
OLS Regression Results
==============================================================================
Dep. Variable: Italy R-squared: 0.706
Model: OLS Adj. R-squared: 0.696
Method: Least Squares F-statistic: 68.97
Date: Sun, 11 Aug 2024 Prob (F-statistic): 1.16e-29
Time: 22:49:09 Log-Likelihood: 249.08
No. Observations: 120 AIC: -488.2
Df Residuals: 115 BIC: -474.2
Df Model: 4
Covariance Type: nonrobust
================================================================================
coef std err t P>|t| [0.025 0.975]
--------------------------------------------------------------------------------
const -0.0005 0.003 -0.161 0.873 -0.006 0.005
FX USD/EUR 0.5203 0.098 5.301 0.000 0.326 0.715
EUR 10Y Rate -0.0382 0.068 -0.566 0.573 -0.172 0.096
CRB Index 0.0835 0.063 1.335 0.185 -0.040 0.207
MSCI World 1.0161 0.069 14.727 0.000 0.879 1.153
==============================================================================
Omnibus: 17.824 Durbin-Watson: 2.452
Prob(Omnibus): 0.000 Jarque-Bera (JB): 76.127
Skew: -0.185 Prob(JB): 2.95e-17
Kurtosis: 6.884 Cond. No. 35.2
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
================================ Spain =================================
OLS Regression Results
==============================================================================
Dep. Variable: Spain R-squared: 0.737
Model: OLS Adj. R-squared: 0.727
Method: Least Squares F-statistic: 80.38
Date: Sun, 11 Aug 2024 Prob (F-statistic): 2.13e-32
Time: 22:49:09 Log-Likelihood: 248.77
No. Observations: 120 AIC: -487.5
Df Residuals: 115 BIC: -473.6
Df Model: 4
Covariance Type: nonrobust
================================================================================
coef std err t P>|t| [0.025 0.975]
--------------------------------------------------------------------------------
const 0.0057 0.003 1.964 0.052 -4.98e-05 0.011
FX USD/EUR 0.5245 0.098 5.330 0.000 0.330 0.719
EUR 10Y Rate -0.0898 0.068 -1.325 0.188 -0.224 0.044
CRB Index -0.1187 0.063 -1.893 0.061 -0.243 0.006
MSCI World 1.1800 0.069 17.060 0.000 1.043 1.317
==============================================================================
Omnibus: 2.041 Durbin-Watson: 2.419
Prob(Omnibus): 0.360 Jarque-Bera (JB): 1.545
Skew: 0.162 Prob(JB): 0.462
Kurtosis: 3.451 Cond. No. 35.2
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
================================ Netherlands =================================
OLS Regression Results
==============================================================================
Dep. Variable: Netherlands R-squared: 0.806
Model: OLS Adj. R-squared: 0.799
Method: Least Squares F-statistic: 119.4
Date: Sun, 11 Aug 2024 Prob (F-statistic): 5.33e-40
Time: 22:49:09 Log-Likelihood: 261.80
No. Observations: 120 AIC: -513.6
Df Residuals: 115 BIC: -499.7
Df Model: 4
Covariance Type: nonrobust
================================================================================
coef std err t P>|t| [0.025 0.975]
--------------------------------------------------------------------------------
const 0.0011 0.003 0.428 0.669 -0.004 0.006
FX USD/EUR 0.4316 0.088 4.889 0.000 0.257 0.606
EUR 10Y Rate 0.0570 0.061 0.939 0.350 -0.063 0.177
CRB Index -0.0364 0.056 -0.647 0.519 -0.148 0.075
MSCI World 1.2156 0.062 19.588 0.000 1.093 1.339
==============================================================================
Omnibus: 1.008 Durbin-Watson: 2.216
Prob(Omnibus): 0.604 Jarque-Bera (JB): 0.703
Skew: -0.179 Prob(JB): 0.704
Kurtosis: 3.110 Cond. No. 35.2
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
================================ Austria =================================
OLS Regression Results
==============================================================================
Dep. Variable: Austria R-squared: 0.607
Model: OLS Adj. R-squared: 0.593
Method: Least Squares F-statistic: 44.37
Date: Sun, 11 Aug 2024 Prob (F-statistic): 1.75e-22
Time: 22:49:09 Log-Likelihood: 200.34
No. Observations: 120 AIC: -390.7
Df Residuals: 115 BIC: -376.7
Df Model: 4
Covariance Type: nonrobust
================================================================================
coef std err t P>|t| [0.025 0.975]
--------------------------------------------------------------------------------
const 0.0020 0.004 0.468 0.641 -0.007 0.011
FX USD/EUR 1.1376 0.147 7.721 0.000 0.846 1.429
EUR 10Y Rate 0.1561 0.101 1.540 0.126 -0.045 0.357
CRB Index 0.3184 0.094 3.391 0.001 0.132 0.504
MSCI World 0.9502 0.104 9.176 0.000 0.745 1.155
==============================================================================
Omnibus: 6.503 Durbin-Watson: 1.871
Prob(Omnibus): 0.039 Jarque-Bera (JB): 11.138
Skew: -0.004 Prob(JB): 0.00382
Kurtosis: 4.492 Cond. No. 35.2
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.